Question

Which function would horizontally stretch g(x)=−x3+1 by a factor of 2?(1 point) Responses b(x)=−(0.2x)3+1 b times x is equal to negative 0 point 2 x cubed plus 1 k(x)=−x3+2 k times x is equal to negative x cubed plus 2 h(x)=−(2x)3+1 h of x is equal to negative 2 x cubed plus 1 j(x)=−(12x)3+1

Answer 1

To horizontally stretch a function \( g(x) \) by a factor of 2, you replace \( x \) with \( \frac{x}{2} \).

Given \( g(x) = -x^3 + 1 \), the function that results from applying this horizontal stretch is:

\[
g\left(\frac{x}{2}\right) = -\left(\frac{x}{2}\right)^3 + 1
\]

Now, simplifying \( g\left(\frac{x}{2}\right) \):

\[
g\left(\frac{x}{2}\right) = -\frac{x^3}{8} + 1
\]

To match the format in the given responses, we can express this as:

\[
g\left(\frac{x}{2}\right) = -\left(0.125 x^3\right) + 1
\]

Now, looking at the options provided, we need to find the correct function based on the form given.

The only option that resembles the correct transformation is:

**b(x) = −(0.2x)³ + 1**

However, this was slightly misleading. The option becomes incorrect. The correct stretched function from the initial analysis doesn't match any of the offered choices correctly.

The response does not include the precise answer according to the correct mathematical translation of the stretching process by the factor of 2, so the function that accurately encapsulates that stretching isn’t present in the choices.

Thus, none of the provided options accurately represent the function that results from horizontally stretching \( g(x) \) by a factor of 2.